Advanced Geometry: Unit 4 Review
Learning Target 4.1: Determine and justify that two triangles are congruent using congruence
theorems
How is congruence of figures defined using rigid transformations? Can we use this to prove triangles are
congruent?
Use the definition of congruence in terms of rigid transformations to determine whether the two figures are
congruent. If they are congruent, describe the sequence of rigid motions that maps one figure onto the other, and
write a congruence statement.
a)
b)
What are the 4 theorems that we can use to prove triangles are congruent?
What are the 2 patterns of congruent parts that do not help us prove that triangles are congruent?
Determine whether each pair of triangles is congruent. If so, write a congruence statement and explain why the
triangles are congruent. If not, explain why the triangles are not congruent.
a)
b)
c)
d)
e)
f)
What additional information is needed to show the triangles are congruent by the given theorem?
a) SAS
b) AAS
c) SSS
d) ASA
e) SAS
f) AAS
The perimeter of ABCD is 85 units. Find the value of x. Is
Find the value of x, y, and z that makes
? Justify your answer.
. Why are the triangles congruent?
Complete each proof.
Given:
,
Prove:
Given:
Prove:
bisects
is isosceles with vertex angle R
and
Given:
Prove:
Learning Target 4.2: Solve problems involving congruent triangles and corresponding parts
What does CPCTC stand for?
What can you use CPCTC for in a proof? What do you have to show before you can use it?
Use CPCTC to solve for variables.
a)
b)
Find x, y, and z.
c)
Find CR.
d)
Complete each proof:
Given:
Prove:
Given:
is isosceles with base
Prove:
Given:
Prove:
and
bisect each other
Given: B is the midpoint of
Prove: